Extra 4 / 12 · Structure
Curve joins and continuity
Two drawn sections meet at one shared endpoint. A smooth-looking join can hide a stronger mismatch, especially when the path will guide motion or further construction.
Selected result
What remains connected
What is checked, and where this example stops
Endpoint displacement and first-derivative displacement are zero. Second-derivative displacement is (0, 6) under the shared normalized parameter. A zero derivative is not accepted as a regular tangent.
C1 and C2 here refer to the same declared parameter. Curvature is a separate open relationship requiring a metric and regularity evidence.